This study will test the hypothesis that a more intensive chemotherapeutic program can improve survival rates in children with high-risk neuroblastoma. The main goals of this study are to determine the maximum tolerated dose of a combination of cyclophosphamide, carboplatin, and etoposide for 3 consecutive courses following 2 courses of a fixed dose of high dose cyclophosphamide, doxorubicin and vincritine given on a 21 day schedule using G-CSF in combination with peripheral blood stem cells; and to determine the disease-free survival rates.